SOLUTION: 1) how do u write an equation in slope-intercept form of the line that passes through (2,-7) and is parallel to the graph of y=x-2? 2) (2,3), y=x+5 3) (-5,-4), 2x+3

Algebra ->  Equations -> SOLUTION: 1) how do u write an equation in slope-intercept form of the line that passes through (2,-7) and is parallel to the graph of y=x-2? 2) (2,3), y=x+5 3) (-5,-4), 2x+3      Log On


   

Question 119809:
1) how do u write an equation in slope-intercept form of the line that passes through (2,-7) and is parallel to the graph of y=x-2?

2) (2,3), y=x+5


3) (-5,-4), 2x+3y=-1
Found 2 solutions by jim_thompson5910, checkley71:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 1 (its from the slope of y=1%2Ax-2 which is also 1). Also since the unknown line goes through (2,-7), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B7=1%2A%28x-2%29 Plug in m=1, x%5B1%5D=2, and y%5B1%5D=-7



y%2B7=1%2Ax-%281%29%282%29 Distribute 1



y%2B7=1%2Ax-2 Multiply



y=1%2Ax-2-7Subtract -7 from both sides to isolate y

y=1%2Ax-9 Combine like terms

So the equation of the line that is parallel to y=1%2Ax-2 and goes through (2,-7) is y=1%2Ax-9


So here are the graphs of the equations y=1%2Ax-2 and y=1%2Ax-9



graph of the given equation y=1%2Ax-2 (red) and graph of the line y=1%2Ax-9(green) that is parallel to the given graph and goes through (2,-7)









#1

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 1 (its from the slope of y=1%2Ax%2B5 which is also 1). Also since the unknown line goes through (2,3), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-3=1%2A%28x-2%29 Plug in m=1, x%5B1%5D=2, and y%5B1%5D=3



y-3=1%2Ax-%281%29%282%29 Distribute 1



y-3=1%2Ax-2 Multiply



y=1%2Ax-2%2B3Add 3 to both sides to isolate y

y=1%2Ax%2B1 Combine like terms

So the equation of the line that is parallel to y=1%2Ax%2B5 and goes through (2,3) is y=1%2Ax%2B1


So here are the graphs of the equations y=1%2Ax%2B5 and y=1%2Ax%2B1



graph of the given equation y=1%2Ax%2B5 (red) and graph of the line y=1%2Ax%2B1(green) that is parallel to the given graph and goes through (2,3)









#3






First convert the standard equation 2x%2B3y=-1 into slope intercept form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


2x%2B3y=-1 Start with the given equation


2x%2B3y-2x=-1-2x Subtract 2x from both sides


3y=-2x-1 Simplify


%283y%29%2F%283%29=%28-2x-1%29%2F%283%29 Divide both sides by 3 to isolate y


y+=+%28-2x%29%2F%283%29%2B%28-1%29%2F%283%29 Break up the fraction on the right hand side


y+=+%28-2%2F3%29x-1%2F3 Reduce and simplify


The original equation 2x%2B3y=-1 (standard form) is equivalent to y+=+%28-2%2F3%29x-1%2F3 (slope-intercept form)


The equation y+=+%28-2%2F3%29x-1%2F3 is in the form y=mx%2Bb where m=-2%2F3 is the slope and b=-1%2F3 is the y intercept.








Now let's find the equation of the line that is parallel to y=%28-2%2F3%29x-1%2F3 which goes through (-5,-4)

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is -2%2F3 (its from the slope of y=%28-2%2F3%29%2Ax-1%2F3 which is also -2%2F3). Also since the unknown line goes through (-5,-4), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B4=%28-2%2F3%29%2A%28x%2B5%29 Plug in m=-2%2F3, x%5B1%5D=-5, and y%5B1%5D=-4



y%2B4=%28-2%2F3%29%2Ax%2B%282%2F3%29%28-5%29 Distribute -2%2F3



y%2B4=%28-2%2F3%29%2Ax-10%2F3 Multiply



y=%28-2%2F3%29%2Ax-10%2F3-4Subtract -4 from both sides to isolate y

y=%28-2%2F3%29%2Ax-10%2F3-12%2F3 Make into equivalent fractions with equal denominators



y=%28-2%2F3%29%2Ax-22%2F3 Combine the fractions



y=%28-2%2F3%29%2Ax-22%2F3 Reduce any fractions

So the equation of the line that is parallel to y=%28-2%2F3%29%2Ax-1%2F3 and goes through (-5,-4) is y=%28-2%2F3%29%2Ax-22%2F3


So here are the graphs of the equations y=%28-2%2F3%29%2Ax-1%2F3 and y=%28-2%2F3%29%2Ax-22%2F3



graph of the given equation y=%28-2%2F3%29%2Ax-1%2F3 (red) and graph of the line y=%28-2%2F3%29%2Ax-22%2F3(green) that is parallel to the given graph and goes through (-5,-4)

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
Y=mX+b HERE WE HAVE A SLOPE OF 1 & X,Y VALUES OF (2,-7) SO WE USE THESE VALUES IN THE LINE EQUATION & SOLVE FOR b THE Y INTYERCEPT.
1) -7=1*2+b
-7=2+b
b=-7-2
b=-9
SO THE LINE EQUATION IS:
Y=X-9
-----------------------------------
2) Y=X+5 (2,3)
3=2*1+b
3=2+b
b=3-2
b=1
SO THE LINE EQUATION IS:
Y=X+1
-----------------------------------------
3) 2X+3Y=-1 (-5,-4)
3Y=-2X-1
Y=-2X/3-1/3
-4=-2/3*-5+b
-4=10/3+b
b=-4-10/3
b=(-12-10)/3
b=-22/3
SO THE LINE EQUATION IS:
Y=-2X/3-22/3